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Complex Analysis, Operators, and Related Topics : The S. A. Vinogradov Memorial Volume :  The S. A. Vinogradov Memorial Volume - Viktor Petrovich Khavin

Complex Analysis, Operators, and Related Topics : The S. A. Vinogradov Memorial Volume

The S. A. Vinogradov Memorial Volume

By: Viktor Petrovich Khavin (Editor), N. K. Nikol'skii (Editor)

Hardcover Published: January 2000
ISBN: 9783764362140
Number Of Pages: 408

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This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. It consists of 30 carefully selected surveys and research papers. The main subjects of the volume include: · free interpolation by analytic functions in its development from the pathbreaking works by L. Carleson up to the most recent achievements and in its connections with the theory of singular integral operators and Carleson-type embedding theorems, moment problems etc. · Szökefalvi-Nagy-Foias model spaces studied from the point of view of holomorphic spaces · holomorphic spaces (Hardy, Bergman, Hölder, and Sobolev spaces) · analytic functions smooth up to the boundary with their subtle properties related to the Nevanlinna-Smirnov factorization, division and multiplication, and zero sets · a new approach to weighted inequalities for singular integrals based on the Bellman function in optimization theory; · the uncertainty principle in harmonic analysis and, in particular, a complete version of Turan's lemma on trigonometric sums · Hankel operators and stationary Gaussian processes · Fourier multipliers, and spectral analysis of some differential operators. These themes are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques. The book is dedicated to the memory of S. A. Vinogradov. It contains a bibliographical note (with a lively portrait) of S. A. Vinogradov, a detailed survey of his mathematical achievements, and a complete list of publications, as well as the translations of two of Vinogradov's surveys whose Russian originals are now hardly accessible.

Stanislav Aleksandrovich Vinogradov, his life and mathematicsp. 1
List of publications of S. A. Vinogradovp. 19
Interpolation problems for analytic functions continuous in the closed disk and for functions whose sequence of coefficients is in l[superscript p]p. 23
Free interpolation in spaces of analytic functionsp. 31
On embedding theorems for coinvariant subspaces of the shift operator, Ip. 45
Continuous and compact embeddings between star-invariant subspacesp. 65
Rational functions in Bergman spacesp. 77
S. A. Vinogradov, as I remember himp. 95
The Bellman functions and sharp weighted inequalities for square functionsp. 97
Multiplicative chaos and multimeasuresp. 115
Some remarks to problems of approximation with prescribed ratep. 127
Interpolation involving bounded bianalytic functionsp. 135
Carleson's interpolation theorem deduced from a result of Pickp. 151
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783764362140
ISBN-10: 3764362146
Series: Operator Theory, Advances and Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 408
Published: January 2000
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.39 x 15.6  x 2.39
Weight (kg): 0.77

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